超立方体网络的(d,k)独立数和(d,k)控制数

ON(d,k)-INDEPENDENCE NUMBER AND(d,k)-DOMINATION NUMBER OF HYPERCUBE NETWORK

(d,k)独立数和(d,k)控制数是分析互连网络性能的重要参数.主要确定了k维超立方体网络的(k-t,k)独立数等于2,如果0≤3t≤k-4,以及(2,k)控制数为2k,如果k≥3.该结论推广了参考文献[6]中的结果,他们的结果(参考文献[6]中的定理3和定理4)是本文定理2当t=0和t=1时的特例.

The （d,k） -independence number and （d,k） -domination number of a connected graph G is an important parameter for analyzing performance of interconnection networks. This paper mainly determines that （k - t,k） - independence number of the k - dimensional hypercube network is equal to two for 0 ≤ 3t ≤ k - 4 ; and also （ 2 ,k） - domination number of the k - dimensional hypercube network is equal to 2k for k≥3. It extends the results of reference [ 6 ] , whose theorem 3 and theorem 4 are exceptions of theorem 2 of this paper when t = 0 and t = 1.